The seventh-placed Turin side lie five points behind Udinese, who are in the fourth and final Champions League qualifying spot with two games left, and Juve are not even assured of playing Europa League football next term in their as yet unnamed new stadium.
The point means mid-table Chievo are now safe from relegation.
But such is the twice European champions's brittle confidence after two seasons of woe that few fans in the nervous Stadio Olimpico were surprised when the visitors retaliated.
Juventus boss Luigi Del Neri, who famously coached Chievo to great success in the previous decade, is fighting to keep his job amid media speculation linking Italy's most successful domestic club with a host of managers including Napoli's Walter Mazzarri.
